Difference between revisions of "ApCoCoA-1:BB.GenHomMultMat"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>BB.GenHomMultMat</title> | <title>BB.GenHomMultMat</title> | ||
| − | <short_description> | + | <short_description>Computes a generic homogeneous multiplication matrix.</short_description> |
<syntax> | <syntax> | ||
| Line 7: | Line 8: | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Computes the generic homogeneous multiplication matrix for x[I] with respect to an order ideal. The inputs are an integer I and a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is a matrix of size <ref>Len</ref>(OO) x <ref>Len</ref>(OO) over the ring BBS=K[c_{ij}]. | + | Computes the generic homogeneous multiplication matrix for <tt>x[I]</tt> with respect to an order ideal. The inputs are an integer <tt>I</tt> and a list <tt>OO</tt> of terms that specify an order ideal. The second element of <tt>OO</tt> must be a non-constant polynomial. The output is a matrix of size <ref>CoCoA:Len|Len</ref>(OO) x <ref>CoCoA:Len|Len</ref>(OO) over the ring <tt>BBS=K[c_{ij}]</tt>. |
<itemize> | <itemize> | ||
| − | <item>@param <em>I</em> | + | <item>@param <em>I</em> An integer which specifies the indeterminate for which the generic homogeneous multiplication matrix will be computed.</item> |
<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
| − | <item>@return The generic homogeneous multiplication matrix | + | <item>@return The generic homogeneous multiplication matrix.</item> |
</itemize> | </itemize> | ||
| + | <example> | ||
| + | Use QQ[x, y, z], DegRevLex; | ||
| + | BB.GenHomMultMat(1, [1, x, x^2, y, z]); | ||
| + | |||
| + | ------------------------------- | ||
| + | Mat([ | ||
| + | [0, 0, 0, 0, 0], | ||
| + | [1, 0, 0, 0, 0], | ||
| + | [0, 1, 0, BBS :: c[3,5], BBS :: c[3,3]], | ||
| + | [0, 0, 0, 0, 0], | ||
| + | [0, 0, 0, 0, 0] | ||
| + | ]) | ||
| + | ------------------------------- | ||
| + | </example> | ||
</description> | </description> | ||
<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| + | <type>matrix</type> | ||
</types> | </types> | ||
<key>GenHomMultMat</key> | <key>GenHomMultMat</key> | ||
<key>BB.GenHomMultMat</key> | <key>BB.GenHomMultMat</key> | ||
<key>borderbasis.GenHomMultMat</key> | <key>borderbasis.GenHomMultMat</key> | ||
| − | <wiki-category>Package_borderbasis</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:40, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.GenHomMultMat
Computes a generic homogeneous multiplication matrix.
Syntax
BB.GenHomMultMat(I:INT,OO:LIST):MAT
Description
Computes the generic homogeneous multiplication matrix for x[I] with respect to an order ideal. The inputs are an integer I and a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is a matrix of size Len(OO) x Len(OO) over the ring BBS=K[c_{ij}].
@param I An integer which specifies the indeterminate for which the generic homogeneous multiplication matrix will be computed.
@param OO A list of terms representing an order ideal.
@return The generic homogeneous multiplication matrix.
Example
Use QQ[x, y, z], DegRevLex; BB.GenHomMultMat(1, [1, x, x^2, y, z]); ------------------------------- Mat([ [0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, BBS :: c[3,5], BBS :: c[3,3]], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0] ]) -------------------------------
